2^{2x-1}=3^{x+2}

Lösung

2^{2 x - 1} = 3^{x + 2}

x = \frac{ln ( 18 )}{2 ln ( 2 ) - ln ( 3 )}

Dezimale

x = 10.04710 \dots

Schritte zur Lösung

2^{2 x - 1} = 3^{x + 2}

Wende Exponentenregel an

(2 x - 1) ln (2) = (x + 2) ln (3)

Löse

(2 x - 1) ln (2) = (x + 2) ln (3) : x = \frac{ln ( 18 )}{2 ln ( 2 ) - ln ( 3 )}

x = \frac{ln ( 18 )}{2 ln ( 2 ) - ln ( 3 )}

so l v e f or x, f = (\frac{1}{2})^{x}

8^{x^{2} - x} = 4^{x + 1}

e^{2 x} = \frac{1}{8}

m e^{m x} + 2 e^{m x} = 0

(100)^{x} = 0